model [T. I. Andersen et al. Nature (London) 638, 79 (2025)]. We focus on the quantum Kibble-Zurek (KZ) mechanism near the quantum critical point. Using the infinite projected entangled pair state, we simulate an infinite lattice and demonstrate the KZ scaling hypothesis for the

XX

correlations across a wide range of ramp times. We use the time-dependent variational principle algorithm to simulate a finite

8\ifmmode\times\else\texttimes\fi{}8

lattice, similar to the one in the quantum simulation, and find that adiabatic finite-size effects dominate for longer ramp times, where the correlation length's growth with increasing ramp time saturates and the excitation energy's dependence on the ramp time crosses over to a power-law decay characteristic of adiabatic transitions. This finding contradicts the quantum simulation data where the correlation length seems to obey KZ-like power laws, although with modified exponents.

DOI: 10.1103/s2fc-3d18

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XX

XX

correlations across a wide range of ramp times. We use the time-dependent variational principle algorithm to simulate a finite

8\ifmmode\times\else\texttimes\fi{}8

Kibble-Zurek dynamical scaling hypothesis in the Google analog-digital quantum simulator of the

XX

model

XX

model [T.I. Andersen \textit{et al.}, Nature (London) \textbf{638}, 79 (2025)]. We focus on the quantum Kibble-Zurek (KZ) mechanism near the quantum critical point. Using the infinite projected entangled pair state, we simulate an infinite lattice and demonstrate the KZ scaling hypothesis for the

XX

correlations across a wide range of ramp times. We use the time-dependent variational principle algorithm to simulate a finite

8\times 8

z

being estimated for two- and three-dimensional Ising models under the usual Metropolis dynamics. These values of

z

are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both two- and three-dimensional spaces.